SOLUTION: the sum of a two-digit number is 8. the number with its digits interchanged is 11 times the original units digit. find the original number.

Question 943310: the sum of a two-digit number is 8. the number with its digits interchanged is 11 times the original units digit. find the original number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let a = the 10's digit
let b = the units
then
10a+b = "the number"
and
10b+a = the number reversed
:
the sum of a two-digit number is 8.
a + b = 8
the number with its digits interchanged is 11 times the original units digit.
10b + a = 11b
a - 11b + 10b = 0
a - b = 0
Use this with the first equation for elimination
a + b = 8
a - b = 0
------------Addition eliminates b, find a
2a = 8
a = 4
Find b
4 + b = 8
b = 4
:
44 is the original number.
:
:
Check this in the statement
"the number with its digits interchanged is 11 times the original units digit
44 = 11(4)
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